Low-energy features of SU(2) Yang-Mills theory with light gluinos

We report on the latest results of the low-lying spectrum of bound states in SU(2) Yang-Mills theory with light gluinos. The behavior of the disconnected contributions in the critical region is analyzed. A first investigation of a three-gluino state is also discussed.Comment: Talk presented at LATTICE99(Higgs, Yukawa, SUSY), Pisa (Italy),3 pages; to be published in Nucl. Phys. B (Proc. Suppl.

Sharp

Poetry by Kasey Kirchner

On the concept of effective temperature in current carrying quantum critical states

Quantum criticality has attracted considerable attention both theoretically and experimentally as a way to describe part of the phase diagram of strongly correlated systems. A scale-invariant fluctuation spectrum at a quantum critical point implies the absence of any intrinsic scale. Any experimental probe may therefore create an out-of-equilibrium setting; the system would be in a non-linear response regime, which violates the fluctuation-dissipation theorem. Here, we study this violation and related out-of equilibrium phenomena in a single electron transistor with ferromagnetic leads, which can be tuned through a quantum phase transition. We review the breakdown of the fluctuation-dissipation theorem and study the universal behavior of the fluctuation dissipation relation of various correlators in the quantum critical regime. In particular, we explore the concept of effective temperature as a means to extend the fluctuation-dissipation theorem into the non-linear regime.Comment: 4 pages, 2 figures; Manuscript for Proceedings of the International Conference on Quantum Criticality and Novel Phases (QCNP09, Dresden

Termination of rewriting strategies: a generic approach

We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying narrowing and abstracting steps. The induction principle is applied through the abstraction mechanism, where terms are replaced by variables representing any of their normal forms. The induction ordering is not given a priori, but defined with ordering constraints, incrementally set during the proof. Abstraction constraints can be used to control the narrowing mechanism, well known to easily diverge. The generic method is then instantiated for the innermost, outermost and local strategies.Comment: 49 page

The rational SPDE approach for Gaussian random fields with general smoothness

A popular approach for modeling and inference in spatial statistics is to represent Gaussian random fields as solutions to stochastic partial differential equations (SPDEs) of the form $L^{\beta}u = \mathcal{W}$, where $\mathcal{W}$ is Gaussian white noise, $L$ is a second-order differential operator, and $\beta>0$ is a parameter that determines the smoothness of $u$. However, this approach has been limited to the case $2\beta\in\mathbb{N}$, which excludes several important models and makes it necessary to keep $\beta$ fixed during inference. We propose a new method, the rational SPDE approach, which in spatial dimension $d\in\mathbb{N}$ is applicable for any $\beta>d/4$, and thus remedies the mentioned limitation. The presented scheme combines a finite element discretization with a rational approximation of the function $x^{-\beta}$ to approximate $u$. For the resulting approximation, an explicit rate of convergence to $u$ in mean-square sense is derived. Furthermore, we show that our method has the same computational benefits as in the restricted case $2\beta\in\mathbb{N}$. Several numerical experiments and a statistical application are used to illustrate the accuracy of the method, and to show that it facilitates likelihood-based inference for all model parameters including $\beta$.Comment: 28 pages, 4 figure